Extended gravity from noncommutativity

TL;DR

This paper reviews a noncommutative gravity theory using the vierbein formalism, showing how it extends classical gravity with higher derivative and curvature terms depending on noncommutativity, and recovers standard gravity when noncommutativity vanishes.

Contribution

It presents a first order noncommutative gravity theory coupled to fermions, derived via the Seiberg-Witten map, including explicit Lorentz invariant correction terms.

Findings

Noncommutative corrections introduce higher derivatives and curvature powers.

The theory reduces to standard gravity with fermions when noncommutativity is zero.

First nontrivial Lorentz invariant corrections are explicitly formulated.

Abstract

We review the first order theory of gravity (vierbein formulation) on noncommutative spacetime studied in [1, 2]. The first order formalism allows to couple the theory to fermions. This NC action is then reinterpreted (using the Seiberg-Witten map) as a gravity theory on commutative spacetime that contains terms with higher derivatives and higher powers of the curvature and depend on the noncommutativity parameter \theta. When the noncommutativity is switched off we recover the usual gravity action coupled to fermions. The first nontrival corrections to the usual gravity action coupled to fermions are presented in a manifest Lorentz invariant form.